This K99/R00 proposal is focused on investigating the protein interactions driving the nucleation of the clathrin-coated vesicles used in clathrin-mediated endocytosis. The main goal of this proposal is to determine the mechanisms of coat nucleation and identify the minimum core set of proteins (out of dozens of implicated proteins) that is necessary and sufficient to nucleate a clathrin coat. The computational model developed here must (1) determine the functions of the many participants in coat nucleation, (2) reproduce experimental properties of the system modeled, and (3) be readily interpretable to guide further experiments and models. Each of the three specific aims has a K99 phase component that provides direct training and experience for these three requirements of the R00 phase of the research. In the K99 phase of my first aim, I develop a limited reaction-diffusion (RD) model of clathrin coat nucleation that captures the interactions between a strongly implicated subset of five proteins and one lipid. This model includes both spatial as well as dynamic detail. The K99 phase of the second aim optimizes the parameters of the model to agree with new liposome binding experiments on the same subset of proteins. In the K99 phase of the third aim, we will create simplified maps of complex, highly detailed simulations (e.g., simulations of biological processes like coat nucleation) using a coarse master equation framework. As a test case for the method, we will study the mechanisms of folding in a beta hairpin protein. In the R00 phase I will develop the reaction-diffusion model to quantify how the sequence of protein associations that lead to coat nucleation depends on the protein and lipid concentrations, as well as to isolate the unique protein subsets that couple with specific transmembrane cargoes to form vesicles. The model will be continually optimized to match experiment as more proteins are introduced to the model, and the results will be analyzed using the master-equation framework of Aim 3. The K99 projects will be completed before the end of one year working with Dr. Gerhard Hummer at the NIH and collaborating with Dr. Linton Traub at University of Pittsburgh. The study of clathrin-mediated endocytosis and the development of the RD software package will consume the first three years of the independent position. This proposal integrates computational and theoretical biophysics with studies of systems-level biological processes.